A ray of ligh is incident at an angle of incidence \(60^{\circ}\) on the glass slab of refractive index \(\sqrt{3}\). After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is \(4 \sqrt{3} \,cm\). The thickness of the glass slab is. . . .. . \(cm\).

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(C) \(12\)

Step-by-step Solution

Detailed explanation

\(\ell= t \sin i \left[1-\frac{\operatorname{cosi}}{\sqrt{\mu^{2}-\sin ^{2} i}}\right]\)

\(\Rightarrow 4 \sqrt{3}= t \sin 60^{\circ}\left[1-\frac{\cos 60^{\circ}}{\sqrt{3-\frac{3}{4}}}\right]\)

Same subject

Three blocks \(A\), \(B\) and \(C\) are pulled on a horizontal smooth surface by a force of \(80 \mathrm{~N}\) as shown in figure. The tensions \(T_1\) and \(T_2\) in the string are respectively _______ and _______.

JEE Mains 2024 Hard
Both the diodes used in the circuit shown are assumed to be ideal and have negligible resistance when these are forward biased. Built in potential in each diode is \(0.7\; \mathrm{V} .\) For the input voltages shown in the figure, the voltage (in \(Volts\)) at point \(A\) is

JEE Mains 2020 Medium
Two radioactive substances \(X\) and \(Y\) originally have \(N _{1}\) and \(N _{2}\) nuclei respectively. Half life of \(X\) is half of the half life of \(Y\). After three half lives of \(Y\), number of nuclei of both are equal. The ratio \(\frac{ N _{1}}{ N _{2}}\) will be equal to

JEE Mains 2021 Hard
The dimensional formula of \(\dfrac{1}{2}\epsilon_0 E^2\) (\(\epsilon_0\) = permittivity of vacuum and \(E\) = electric field) is \(M^a L^b T^c\). The value of \(2a - b + c = \) _______.

JEE Mains 2026 Medium
A massless spring gets elongated by amount \(x_1\) under a tension of 5 N . Its elongation is \(x_2\) under the tension of 7 N . For the elongation of \(\left(5 x_1-2 x_2\right)\), the tension in the spring will be,

JEE Mains 2025 Easy
A tennis ball (treated as hollow spherical shell) starting from \(O\) rolls down a hill. At point \(A\) the ball becomes air borne leaving at an angle of \(30^o\) with the horizontal. The ball strikes the ground at \(B\). What is the value of the distance \(AB\) ? (Moment of inertia of a spherical shell of mass \(m\) and radius \(R\) about its diameter .......... \(m\). \(= \frac {2}{3}\,mR^2\))

JEE Mains 2013 Hard

Explore more questions on app

From JEE Mains

A Laser light of wavelength \(660\,nm\) is used to weld Retina detachment. If a Laser pulse of width \(60\, ms\) and power \(0.5\, kW\) is used the approximate number of photons in the pulse are : [Take Planck's constant \(h\, = 6.62\times10^{- 34}\, Js\)]

JEE Mains 2017 Medium
Two cars are travelling towards each other at speed of \(20 \mathrm{~m} \mathrm{~s}^{-1}\) each. When the cars are \(300 \mathrm{~m}\) apart, both the drivers apply brakes and the cars retard at the rate of \(2 \mathrm{~m} \mathrm{~s}^{-2}\). The distance between them when they come to rest is _______.

JEE Mains 2024 Hard
In an \(LC\) oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes \(x\) times its initial resonant frequency \(\omega_0\). The value of \(x\) is:

JEE Mains 2023 Easy
A particle of mass \(m\) is moving along the side of a square of side '\(a\)', with a uniform speed \(v\) in the \(x-y\) plane as shown in the figure Which of the following statement is false for the angular momentum \(\vec L\) about the origin ?

JEE Mains 2016 Hard

Explore more questions on app